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1.
For an arbitrary uniformly continuous completely positive semigroup (
t
:t0) on the space of bounded operators on a Hilbert space, we construct a family (U(t)t0) of unitary operators on a Hilbert space and a conditional expectation from to, such that, for arbitraryt0,. The unitary operatorsU(t) satisfy a stochastic differential equation involving a noncommutative generalisation of infinite dimensional Brownian motion. They do not form a semigroup.Part of this work was completed when the first author was visiting research associate at the Center for Relativity, Physics Department, The University of Texas at Austin, Austin, TX 78712, U.S.A., supported in part by NSF PHY 81-01381. 相似文献
2.
Geoffrey S. Watson 《Annals of the Institute of Statistical Mathematics》1983,35(1):303-319
Summary A distribution on the unit sphere inℝ
q
with a densityf(‖x
v
‖) is considered where
is ans(<q) dimensional subspace andx
v
is the part ofx in
. For a large sample the estimation of
, a test that
and a test for rotational symmetry within
is given. For several samples with possibly different subspaces
but the samef, a test that
is given. For all tests power functions for contiguous alternatives are given. For the special density proportional to expk‖x
v
‖
2, additional results are given.
Research supported in part by a Contract with the Office of Naval Research N00014-81-K-0146 awarded to Princeton University,
Princeton, New Jersey 08544. 相似文献
3.
V. V. Napalkov Jr. 《Mathematical Notes》1996,60(1):42-48
We study the growth of an entire functionƒ, whose Borel transformγƒ is holomorphic outside a bounded convex regionD
ƒ with boundary curvature bounded away from 0 and ∞. The functionγƒ is assumed to belong to the Dirichlet space, i.e., it satisfies
, wheredv(ξ) is the area element. It is shown that forγƒ to satisfy the above conditions, it is necessary and sufficient to have
and the growth indicatrixh
ƒ ofƒ satisfies the relation 0<m≤h″(ϕ)+h(ϕ)≤M<∞.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 58–65, July, 1996. 相似文献
4.
Evgeni Ja. Gabovič 《Semigroup Forum》1972,4(1):335-340
A semigroup S is calledE-semigroup (
-semigroup) if every (finitely generated) subsemigroup of S is an endomorphic image of S and Ē-semigroup (
-semigroup) if every subsemigroup of S is an E-semigroup
-semigroup. All classes X ε {Ē,
, E,
} are distinct even in the case of semilattices. It is established when a free band (semilattice) is an X-semigroup.
-,
- and Ē-chains and E-chains with identity or zero, Ē-and
, X-bands with identity and X-semigroups with identity and zero are found. 相似文献
5.
K. R. Apt 《Israel Journal of Mathematics》1978,29(2-3):221-238
The connections between inductive definability and models of comprehension are studied. Let
= 〈A, R
l, ...,R
n 〉 be an infinite structure and letI
φ
be a set inductively defined by a formulaφ of the second order language
. We prove that if
is a model of Δ
1
1
-Comprehension relativized toφ, andφ is
-absolute, then for everyη smaller than the height of
(h(
)),I
φ
is in
. If
is aβ-structure which satisfies Σ
1
1
-Comprehension relativized toφ and WF(X), and φ is
-absolute, thenI
φ
is in
and ‖φ| <h (
). These results imply that Barwise-Grilliot theorem is false in the case of uncountable acceptable structures. We also study
the notion of invariant definability over models1 of Δ
1
1
-Comprehension.
This paper is registered as Report ZW 69/76 of the Mathematical Centre. 相似文献
6.
We prove a Schwarz lemma for a domain
in ℂ3 that arises in connection with a problem in H∞ control theory. We describe a class of automorphisms of
and determine the distinguished boundary of
We apply our Schwarz lemma to a special case of the μ-synthesis problem. 相似文献
7.
Yongge Tian 《Advances in Applied Clifford Algebras》2000,10(1):61-90
As is well-known, the real quaternion division algebra ℍ is algebraically isomorphic to a 4-by-4 real matrix algebra. But
the real division octonion algebra
can not be algebraically isomorphic to any matrix algebras over the real number field ℝ, because
is a non-associative algebra over ℝ. However since
is an extension of ℍ by the Cayley-Dickson process and is also finite-dimensional, some pseudo real matrix representations
of octonions can still be introduced through real matrix representations of quaternions. In this paper we give a complete
investigation to real matrix representations of octonions, and consider their various applications to octonions as well as
matrices of octonions. 相似文献
8.
This paper introduces the concept of ‘symmetric centres’ of braided monoidal categories. LetH be a Hopf algebra with bijective antipode over a fieldk. We address the symmetric centre of the Yetter-Drinfel’d module category:
and show that a left Yetter-Drinfel’d moduleM belongs to the symmetric centre of
and only ifM is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give
a sufficient and necessary condition for the braid of,
Hℳ to induce the braid of
, or equivalently, the braid of
, whereA is a quantum commutativeH-module algebra 相似文献
9.
J. A. S. Martins 《Annali di Matematica Pura ed Applicata》1977,115(1):271-294
Summary Piecewise polynomial and Fourier approximation of functions in the Sobolev spaces
on unbounded domains Θ ⊂ Rn are applied to the study of the type of compact embeddings into appropriate Lebesgue and Orlicz spaces. It is shown that
if Θ and s satisfy certain conditions, the embeddings
, m/n+1/q−1/p>0 and
, Φ being an Orlicz function subordinate to both φ(t)=|t|p
exp |t|n/(n−m) and Φσ(t)=exp |t|σ−1, σ ⩾ 1, m/n>1/p, are of type ls. One result dealing with multiplications maps from
into Lq(Θ) is also obtained.
Entrata in Redazione il 14 ottobre 1976. 相似文献
10.
Edward W. Barankin Koiti Takahasi 《Annals of the Institute of Statistical Mathematics》1984,36(1):499-520
Summary This paper introduces terminology enabling the discussion of centerrelated betweennesses defined with respect to centers other
than the origin. Thus, it is then proved that the familiar
-betweenness in
which is origin-centered, is equivalent to a non-origin-centered
-betweenness in one lower dimension. A new betweenness inK, denoted by
, (r>0), is defined and studied, and it is shown that its restriction to
is precisely
-betweenness for a certain ν. Finally, by a method elaborated in the earlier papers, a new betweeness,
, is induced on the upper open-hemisphere-plus-a-point in 3-space, and a characterization of it is obtained which is expected
to facilitate later investigations of betweenness is complex spaces. 相似文献
11.
Satoru Fujishige 《Mathematical Programming》1984,29(2):125-141
The present paper shows that for any submodular functionf on a crossing family
with
, if the polyhedron
is nonempty, then there exist a unique distributive lattice
with
and a unique submodular function
with
such thatB(f) coincides with the base polyhedron
associated with the submodular system
. Here, iff is integer-valued, thenf
1 is also integer-valued.
Based on this fact, we also show the relationship between the independent-flow problem considered by the author and the minimum
cost flow problem considered by J. Edmonds and R. Giles. 相似文献
12.
Z. A. Arushanyan 《Journal of Mathematical Sciences》1981,16(3):1161-1167
One finds conditions which ensure the possibility of weighted mean-square approximation of a vector-function defined on the
boundary of an n-dimensional domain
by vector-functions of the form
, where u is, the solution of the equation Δm
u=0 in
while∂/∂v denotes differentiation along the normal. The weight function is continuous and positive everywhere on
with the point
whose relative neighborhood
is contained in some (n-1)-dimensional plane. The solution of this approximation problem is closely related with a certain
uniqueness theorem for the solution of the Cauchy problem for the polyharmonic equation, also proved in the paper.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR,
Vol. 65, pp. 164–171, 1976. 相似文献
13.
Let
be a family of two-valued functions defined on ann-element set in which each pair of functions in
satisfy a given intersection condition. For certain intersection conditions we determine the maximal value of
. 相似文献
14.
Let
, N≧3 be an open set. In this paper we study weak positive solutions of the following semilinear system
where p≧1, q≧1, with pq>1, and u∈Lq(Ω), v∈Lp(Ω), and we give in particular some regularity results. Furthermore, we give some applications to the biharmonic equation.
Entrata in Redazione il 25 febbraio 1999. 相似文献
15.
Cristina Trombetti 《Annali di Matematica Pura ed Applicata》1999,177(1):277-292
Summary We prove the existence of minimizing pairs (K, u), K compact set ofR
N and u∈W1, p (Ω/K), for the functional
when the integrand f(x, z) is convex with respect to z, |z|p≤f(x, z)≤L|z|p, p>1, and satisfies suitable assumptions of uniform continuity in x with respect to z.
Entrata in Redazione il 10 luglio 1998. 相似文献
16.
R. Schneider 《Discrete and Computational Geometry》1995,13(1):609-627
Let
be an infinite discrete system ofk-dimensional flats inn-dimensional Euclidean space. If the totalk-dimensional volume of the flats in
intersected with the ball of center 0 and radiusr, divided by the volume of that ball, tends to a limit forr→∞, then this limit is called thedensity of
. We consider isoperimetric problems of the following kind. If
is a hyperplane system of positive density, find sharp upper bounds for the density of the system ofk-flats (k∈{0, ...,n−2}) that are generated as intersections of hyperplanes in
. Ideas from the theory of uniform distribution of sequences are employed to define a large class of hyperplane systems, calleduniform, for which all necessary densities exist, isperimetric inequalities can be proved, and systems with extremal intersection
densities can be characterized. 相似文献
17.
A monotone structure (
;μ) consists of a structure
and a monotone systemμ over the domain of
.L(Q
n
) is
, enlarged by a newn-ary quantifierQ
n
.
says in (
;μ) that there isU ∈μ such thatϕ[ā] is valid in (
;μ) for allā ∈U
n
. If
is a class of monotone structures,
means thatϕ is valid in all expansions of monotone structures in
. We show for the class
of all ultrafilters that interpolation with respect to
holds forL(Q
n
) exactly in casen=1. Then we prove for a large class of
(e.g. the class of topological groups) thatL(Q
n
) satisfies interpolation with respect to
for alln ≧ 1. Counterexamples indicate that the class of
is sharp in some sense. Finally the results are carried over to certain topological structures and the interior quantifiersI
n
instead ofQ
n
, thereby generalizing results of Makowsky/Ziegler and Sgro, and to a multidimensional type of monotone structures including
uniform spaces. 相似文献
18.
H. Schwerdtfeger 《Annali di Matematica Pura ed Applicata》1961,54(1):23-31
Summary It is shown that the group of all Moebius transformations (M. T.) contains a subgroup
such that every non-involutory M. T. not in
can be transformed into each of its conjugates outside the subgroup
by a unique element of this subgroup. Hence every non-integral and non-involutory M. T. can be reduced into a normal form
by means of a unique element of
. Also a subgroup
*, can be determined such that elements of
* reduce all non-involutory M. T. not in
*, into their classical (integral) normal forms. There is also a discussion of the question as to other fields over which
the results remain valid.
To Enrico Bompiani on his scientific Jubilee. 相似文献
19.
Dionisio Gallarati 《Annali di Matematica Pura ed Applicata》1957,43(1):195-214
Sunto Si dànno delle condizioni necessarie affinchè due superficie algebriche F, G d’una V
3
algebrica non singolare possano presentare contatto d’ordine assegnato q −1 lungo una curva
priva di punti multipli. Si approfondisce sopratuito il caso q=3, con applicazione al problema di determinare le superficie algebriche Gn di S
3
che presentano contatto del 3o ordine lungo una
n con una superficie quartica F
4
. 相似文献
20.
Le Tu Quoc Thang 《Discrete and Computational Geometry》1995,14(1):31-70
The existence of different kinds of local rules is established for many sets of pentagonal quasi-crystal tilings. For eacht∈ℝ there is a set
of pentagonal tilings of the same local isomorphism class; the caset=0 corresponds to the Penrose tilings. It is proved that the set
admits a local rule which does not involve any colorings (or markings, decorations) if and only ift=m+nτ. In other words, this set of tilings is totally characterized by patches of some finite radius, orr-maps. When
the set
admits a local rule which involvescolorings. For the set of Penrose tilings the construction here leads exactly to the Penrose matching rules. Local rules for the caset=1/2 are presented. 相似文献